Using AutoHotkey—which Lowell gave a nice nod to earlier today—derilium whipped up a script (and system tray executable for those of you who don't want to install AHK) that lets you use the Tab key (and Shift+Tab) to quickly move between editing file names in Explorer, just like in the video above. If you want the code itself, it looks like this:

derilium and I had some back-and-forth in the #tips section getting the script hammered out, but the code posted above worked for me. If you give it a go, let's hear how it works for you in the comments. If you just want to download and use the EXE, you can grab it here. Thanks derilium!